D.W. Pearson and M-R. Boudarel (2001)
Pair Interactions : Real and Perceived Attitudes
Journal of Artificial Societies and Social Simulation
vol. 4, no. 4
<https://www.jasss.org/4/4/4.html>
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
Received: 29-Mar-01 Accepted: 30-Sep-01 Published: 31-Oct-01
Figure 1: Pair interaction of two individuals |
(1)
with the boundary conditions u_{ij}(N)x^{N}y=v_{ij}(-N)xij^{N}=0.
(2)
where α_{11}∈[-N,N], α∈[0,1], β≥0 and γ≥0 are parameters and f is a function having a trapezoidal form as shown in figure 2.
Figure 2: Function f |
(3)
(4)
Figure 3: The particular choice of function f |
Figure 4: Initial distribution : biased towards confidence |
Figure 5: Initial distribution : biased towards non-confidence |
Figure 6: Initial distribution : neutral confidence |
Figure 7: Simulation results - confidence levels as experienced by individual 1 |
Figure 8: Simulation results - confidence levels as perceived by individual 1 |
Figure 9: Simulation results - confidence levels as perceived by individual 2 |
Figure 10: Simulation results - confidence levels as experienced by individual 2 |
Figure 11: Simulation results - confidence levels as experienced by individual 1 |
Figure 12: Simulation results - confidence levels as perceived by individual 1 |
Figure 13: Simulation results - confidence levels as perceived by individual 2 |
Figure 14: Simulation results - confidence levels as experienced by individual 2 |
LE CARDINAL, G., GUYONNET, J.-F. and POUZOULLIC (1997), La Dynamique de la Confiance, Dunod.
PEARSON, D.W., ALBERT, P., BESOMBES, B., BOUDEREL, M.-R., MARCON, E. and MNEMOI, G. (2001a), Modelling Enterprise Networks: A Master Equation Approach, to appear European Journal of Operational Research.
PEARSON, D.W. and DRAY, G. (2001b), A Fuzzy Approach to Sociodynamical Interactions, Proceedings International Conference on Artificial Neural Networks and Genetic Algorithms, Prague, Czech Republic.
WEIDLICH, W. and HAAG, G. (1983), Concepts and Models of a Quantitative Sociology, Springer-Verlag.
clear clf N=5; a=[N -N -N N N N N 0]; alpha=[0.9 0.9 1 1 1 1 0.2 0.2]; beta=[2 2 2 2 2 2 2 2]; gamma=[2 2 2 2 0.1 0.1 0.1 0.1]; fp=[1 4 0.5 0.5 1 4 0.5 0.5]; dist1=[0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0.1 ; 0.2 ; 0.4 ; 0.2 ; 0.1]; dist2=[0.1 ; 0.2 ; 0.4 ; 0.2 ; 0.1 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0]; dist3=[0 ; 0 ; 0 ; 0.1 ; 0.2 ; 0.4 ; 0.2 ; 0.1 ; 0 ; 0 ; 0]; x0=[dist1 ; dist2 ; dist2 ; dist1 ; dist1 ; dist1 ; dist1 ; dist3]; [t,x]=ode45('group_interaction',[0,30],x0,[],a,N,alpha,beta,gamma,fp); clf u=-N:N; for j=1:length(t) for i=1:2*N+1 z11(i,j)=x(j,i); z21(i,j)=x(j,2*N+1+i); zhat12(i,j)=x(j,2*(2*N+1)+i); zhat22(i,j)=x(j,3*(2*N+1)+i); zhat11(i,j)=x(j,4*(2*N+1)+i); zhat21(i,j)=x(j,5*(2*N+1)+i); z12(i,j)=x(j,6*(2*N+1)+i); z22(i,j)=x(j,7*(2*N+1)+i); end end for i=1:2*N+1 f(i)=funcf(u(i),fp(1,1),fp(1,2),fp(1,3),fp(1,4),N); end % the world as seen by individual 1 figure(1) subplot(2,1,1) surfl(t,u,z11) xlabel('t') ylabel('confidence') zlabel('x_{11}') shading interp colormap('cool') subplot(2,1,2) surfl(t,u,z21) xlabel('t') ylabel('confidence') zlabel('x_{21}') shading interp colormap('cool') figure(2) subplot(2,1,1) surfl(t,u,zhat12) xlabel('t') ylabel('confidence') zlabel('z_{12}') shading interp colormap('cool') subplot(2,1,2) surfl(t,u,zhat22) xlabel('t') ylabel('confidence') zlabel('z_{22}') shading interp colormap('cool') % the world as seen by individual 2 figure(3) subplot(2,1,1) surfl(t,u,zhat11) xlabel('t') ylabel('confidence') zlabel('z_{11}') shading interp colormap('cool') subplot(2,1,2) surfl(t,u,zhat21) xlabel('t') ylabel('confidence') zlabel('z_{21}') shading interp colormap('cool') figure(4) subplot(2,1,1) surfl(t,u,z12) xlabel('t') ylabel('confidence') zlabel('x_{12}') shading interp colormap('cool') subplot(2,1,2) surfl(t,u,z22) xlabel('t') ylabel('confidence') zlabel('x_{22}') shading interp colormap('cool') The various functions called by the main program function f=funcf(x,n1,n2,f1,f2,N) if x=n1 &
xf(1)=f(1)-uij(x,-N,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(1);
for n=-N+1:N-1 i=n+N+1; f(i)=vij(x,n+1,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i+1 ); f(i)=f(i)-vij(x,n,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); f(i)=f(i)+uij(x,n-1,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i-1); f(i)=f(i)-uij(x,n,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); end f(2*N+1)=-vij(x,N,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*N+1); f(2*N+1)=f(2*N+1)+uij(x,N-1,1,3,4,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*N); % x21 f(2*N+2)=vij(x,-N+1,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*N+3); f(2*N+2)=f(2*N+2)-uij(x,-N,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*N+2); for n=-N+1:N-1 i=n+3*N+2; f(i)=vij(x,n+1,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i+1); f(i)=f(i)-vij(x,n,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); f(i)=f(i)+uij(x,n-1,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i-1); f(i)=f(i)-uij(x,n,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); end f(2*(2*N+1))=-vij(x,N,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*(2*N+1)); f(2*(2*N+1))=f(2*(2*N+1))+uij(x,N-1,2,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*(2*N+1)-1); % z12 f(2*(2*N+1)+1)=vij(x,-N+1,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*(2*N+1)+2); f(2*(2*N+1)+1)=f(2*(2*N+1)+1)-uij(x,-N,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(2*(2*N+1)+1); for n=-N+1:N-1 i=n+2*(2*N+1)+N+1; f(i)=vij(x,n+1,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i+1); f(i)=f(i)-vij(x,n,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); f(i)=f(i)+uij(x,n-1,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i-1); f(i)=f(i)-uij(x,n,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); end f(3*(2*N+1))=-vij(x,N,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(3*(2*N+1)); f(3*(2*N+1))=f(3*(2*N+1))+uij(x,N-1,3,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(3*(2*N+1)-1); % z22 f(3*(2*N+1)+1)=vij(x,-N+1,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(3*(2*N+1)+2); f(3*(2*N+1)+1)=f(3*(2*N+1)+1)-uij(x,-N,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(3*(2*N+1)+1); for n=-N+1:N-1 i=n+3*(2*N+1)+N+1; f(i)=vij(x,n+1,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i+1); f(i)=f(i)-vij(x,n,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); f(i)=f(i)+uij(x,n-1,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i-1); f(i)=f(i)-uij(x,n,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(i); end f(4*(2*N+1))=-vij(x,N,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(4*(2*N+1)); f(4*(2*N+1))=f(4*(2*N+1))+uij(x,N-1,4,3,0,a,N,alpha,beta,gamma,fp(1,1),fp(1,2),fp(1,3),fp(1,4))*x(4*(2*N+1)-1); % z11 f(4*(2*N+1)+1)=vij(x,-N+1,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(4*(2*N+1)+2); f(4*(2*N+1)+1)=f(4*(2*N+1)+1)-uij(x,-N,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(4*(2*N+1)+1); for n=-N+1:N-1 i=n+4*(2*N+1)+N+1; f(i)=vij(x,n+1,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i+1); f(i)=f(i)-vij(x,n,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); f(i)=f(i)+uij(x,n-1,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i-1); f(i)=f(i)-uij(x,n,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); end f(5*(2*N+1))=-vij(x,N,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(5*(2*N+1)); f(5*(2*N+1))=f(5*(2*N+1))+uij(x,N-1,5,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(5*(2*N+1)-1); % z21 f(5*(2*N+1)+1)=vij(x,-N+1,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(5*(2*N+1)+2); f(5*(2*N+1)+1)=f(5*(2*N+1)+1)-uij(x,-N,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(5*(2*N+1)+1); for n=-N+1:N-1 i=n+5*(2*N+1)+N+1; f(i)=vij(x,n+1,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i+1); f(i)=f(i)-vij(x,n,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); f(i)=f(i)+uij(x,n-1,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i-1); f(i)=f(i)-uij(x,n,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); end f(6*(2*N+1))=-vij(x,N,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(6*(2*N+1)); f(6*(2*N+1))=f(6*(2*N+1))+uij(x,N-1,6,3,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(6*(2*N+1)-1); % x12 f(6*(2*N+1)+1)=vij(x,-N+1,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(6*(2*N+1)+2); f(6*(2*N+1)+1)=f(6*(2*N+1)+1)-uij(x,-N,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(6*(2*N+1)+1); for n=-N+1:N-1 i=n+6*(2*N+1)+N+1; f(i)=vij(x,n+1,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i+1); f(i)=f(i)-vij(x,n,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); f(i)=f(i)+uij(x,n-1,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i-1); f(i)=f(i)-uij(x,n,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); end f(7*(2*N+1))=-vij(x,N,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(7*(2*N+1)); f(7*(2*N+1))=f(7*(2*N+1))+uij(x,N-1,7,6,0,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(7*(2*N+1)-1); % x22 f(7*(2*N+1)+1)=vij(x,-N+1,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(7*(2*N+1)+2); f(7*(2*N+1)+1)=f(7*(2*N+1)+1)-uij(x,-N,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(7*(2*N+1)+1); for n=-N+1:N-1 i=n+7*(2*N+1)+N+1; f(i)=vij(x,n+1,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i+1); f(i)=f(i)-vij(x,n,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); f(i)=f(i)+uij(x,n-1,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i-1); f(i)=f(i)-uij(x,n,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(i); end f(8*(2*N+1))=-vij(x,N,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(8*(2*N+1)); f(8*(2*N+1))=f(8*(2*N+1))+uij(x,N-1,8,6,5,a,N,alpha,beta,gamma,fp(2,1),fp(2,2),fp(2,3),fp(2,4))*x(8*(2*N+1)-1); f=f'; function f=uij(x,n,k,l,m,a,N,alpha,beta,gamma,n1,n2,f1,f2) f=alpha(k)*exp(-beta(k)*((n+1-a(k))^2)); if m==0 f=f+(1-alpha(k))*exp(-gamma(k)*((n+1-Exij(x,l,N))^2)); else f=f+(1-alpha(k))*exp(-gamma(k)*((n+1-Exij(x,l,N))^2))*funcf(Exij(x,m,N),n1,n2,f1,f2,N); end function f=vij(x,n,k,l,m,a,N,alpha,beta,gamma,n1,n2,f1,f2) f=alpha(k)*exp(-beta(k)*((n-1-a(k))^2)); if m==0 f=f+(1-alpha(k))*exp(-gamma(k)*((n-1-Exij(x,l,N))^2)); else f=f+(1-alpha(k))*exp(-gamma(k)*((n-1-Exij(x,l,N))^2))*funcf(Exij(x,m,N),n1,n2,f1,f2,N); end
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